The grandfather paradox states that if you go into the past and kill your grandfather you could never have been born. Therefore it would be impossible for you to travel back through time and kill him. However this is solvable once we realize that time is both linear and cyclical. Similar to a racetrack the 'Start, and 'End' of a path or lifespan are the same exact point. It is a cyclical process. However it is also linear in the sense that you are constantly moving 'forwards'. That is our first instance of linear and cyclical time.

In this example your grandfather's first trip around the track resulted in your father's birth and consequently yours. Then your revisit to his life prompts a second loop around the track. This time he experiences alternative events, namely his early death by you. However nothing can take away that first loop that he had.

Therefore the life events or 'driving forwards' along the path are linear events. Combined, those linear events make up a loop or cyclical path. Meanwhile the completion of one loop after the next is a linear process. The two forms of time go from one to the next then back again. From linear to cyclical to linear, and so on and so forth. It's cyclical paths along a linear line that itself is ultimately cyclical, and so on so forth. It's a fractal.

Therefore going back and killing your grandfather would not effect your life. Going back would merely supply him with a secondary alternative lifespan or loop.

Additional: By implementing not just one but to forms of time the Universe is allowing us to travel any direction through time as it does space while keeping it's overall integrity.

Reality is multidimensional. Time appears linear to the ego but to consciousness itself, time is only a construct, rather than a rule that binds consciousness to precepts.Past, present, future, all exist now and no particular reality is THE reality, in that consciousness is not limited to absolute realities but rather traverses multiple probabilities and possibilites within an infinite possible perceptions of any sequence of events.

You could say killing your grandfather might result in never being born, but that would limit your consciousness to one timeline and a set sequence of events. One reality might reflect that possible outcome while another may not.

Being that consciousness is not bound by rules of any particular measure, conceivably you could go back in time and remove your grandfather and still maintain the future as it existed, remaining intact.

We change the past as easily as we create probable futures, or our mind and our experience of something we visit time and time again.

Rules of relative measure do not apply to consciousness. Consciousness applies form and function into relative experience and duality.

Quantum Physics supports this idea thru the Heisenberg principle.Metaphysics supports this thru the study of Self/Consciousness.